Alien Children

The main equation is a branch of the polar equation

r³ - 3r = a(sinθ - abs(cosθ)), where a = 1.4

Its rectangular equation is

(x² + y² - 3)(x² + y²) = 1.4(y - abs(x))

The main equation is a branch of the polar equation

r³ - 3r + 3 = a(e^sinθ + abs(sinθ)^e), where a = 1.45

Its rectangular equation is

(x² + y² - 3) sqrt(x² + y²) + 3

= 1.45(e^(y/sqrt(x² + y²)) + abs(y/sqrt(x² + y²))^e)

( Mathematical software used: gnuplot )